The idea of operating a 146-100 on any route is absurd. Having managed the commercial,operations of the things I know just what a financial disaster they are. To combine them with a thin route like Carlisle to anywhere is a certain way to lose money. Breakeven load factor will be about 200%. But if that is the way they want to throw their money away then let them do it.
As has already been posted Autair did operate the route in the 1960's. Carlisle was a stop en route to Dundee. As I recall it they used the Ambassador. Hopeless and it didn't last long.